JPS6032364B2 - digital filter - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a digital filter, and more particularly to a digital filter capable of processing (radio wave) signal signals.

A complex signal is expressed as X(t)=A(t)ej(■t+gu(t)).

However, t is a time variable, e is the base of the natural logarithm, the angular frequency, and the phase. The compound Qin signal expressed by the above formula is X(t) = A river COS(t+○(t))+
)sin(t10(t)) =×(t)+gold(t).

C(t)=B(t)ej8(t)=B(t)cos8iB(t)smo(t) When the above signal is waved with a filter having an impulse response of Y(t) itself is also a postprime signal.

This signal is also Y(t) It is also written as

In general, the type of furnace wave processing (furnace wave processing) and loading function processing (Y(t))
=C(t)×X(t), and the furnace wave processing when the sampled signal is processed is expressed as N Ym=n≦IXm-non.

This appears before Xm and is the result of N X
This shows that it is derived from the sum of samples of (t). The two components of the waveformed double line signal are each N
To To (1) b-× ym=n3・(xm-nn m-nbn) ◇m=day, (
◇m-.

b. Ten Xm-. public. ) can be derived from the above explanation. A post-element filter that relies on processing according to equations '1' and '2' requires 12 additions and 4N multiplications to sequentially generate waveformed signals, which is a function of N coefficients. This is equivalent to performing four transversal reactor wave processes using , which is extremely expensive.

It is an object of the present invention to provide a filter that significantly reduces the computational power required to perform such furnace wave processing.

In order to more easily understand the present invention, formulas '1} and '2
} First, a normal complex signal filter that performs the calculation as shown in the notation will be explained.

As shown in FIG. 1, sample components xm and xm of the x river are applied to shift registers SRI and SR2, respectively. These registers are equipped with N taps, each tap connected to a corresponding input of two multipliers. The second input of each multiplier is supplied with a coefficient belonging to one of the small b and b of the disease wave coefficient. The sequential outputs from both calculators are N. b ym=n≧・×m-n n n to N-join ym;n≧・×m-n n' ・b Imafu=vine. ~-nn to N to N.b ym=n≧.×mnn They are sequentially added so as to generate n.

After that, two further adders are provided such that ym=ym−
Generate y″m and ym=ym+y″m.

Therefore, such a filter requires the same computational power as a conventional four transversal filter would require.

According to the invention, the same result can be obtained with considerably less computational power. If p is a prime number, then the sequence {《Za》,《《Z》》,...,《gp-1》] is 1 and p-
It is known that there are multiple integers g, called primitive roots of p, that include all numbers between 1 and 1.

In the above representation, each term between double brackets is a term that has a value modulo p. Note first that p-1 is an even number, except when p=2, so the above alignment consists of an even number of integers. This notation field represents all positive and negative integers between te'ma, -gaku and tengo. It is also known that the number system of the present invention has an equivalent value, i.e., real integers belonging to the sequence 1 to p-1. .

If the number i is a real prime number, and if we use only the numbers for which Fermat's number 0, p = 22q11, then , symbol 3 means "takes the same value".

Therefore, 《G mini》3《ノ:T》... (q-・) It is.

In Fermat's number system, the number representing i is represented by a dance of 2, and by simple means of shifting bits, real numbers can be changed to imaginary numbers, and imaginary numbers to real numbers, so when processing binary numbers, is of particular interest.

Therefore, the formula '1' and (to 2-pronged N 〈 〈 2ym=Z
n) ten (xm-n-ixm-n) (bn-ibn)]
(3)nni12j◇m:.

≧, [(X 1j◇) (b. 10j.) − (x −i
◇ ) (b.-j.)] can be transformed into (4), and equivalently 《2ym hometown. [kuXm-n+22kuq-・flame skin)kub.

122 Kuq-1 Duke) 10 KuX -22 Kub. −22(q−
- Popular. )〕》 (5)《2.22(q-, Kuge n≧, [
(xm-n+22(q-・Kamisaki)kub.

122 (q-zu. ◇m-.) (b.-22 (q-1) valley.)]》 (6) Multiplying a word by q-1 means each bit of the word is 2q- This is equivalent to shifting by one bit position. Equations {5- and (2) indicate that the complex signal filter of the present invention can be constructed with half the number of multipliers required in the filter of FIG. The computational power required is the same as that of two transversal filters. An embodiment of the invention is shown in FIG. This embodiment has two inputs to which samples (terms) xm and m are respectively applied. Section meeting m first,
It is delayed by 2q-1 bit times using shift register SR, thus generating i-winter. By simply using adder ADI and subtractor AD2, the terms (xm+i father) and (xm
- m) is obtained. To simplify the explanation of the present invention, it is first assumed that the plurality of wave coefficients of the filter are constant.

When a filter is manufactured, its impulse response C(
Once all the in-phase components bw and six orthogonal components of the above) are determined, it is configured such that the corresponding coefficient values bk and Sk can be derived from these. However, formula '31 to'
6), the signals x(t)+chin(t) and x(t
)-i2(t), the necessary coefficients must be derived from bk-i6k and bk-i6k. In this case, since the term i is a real number, each coefficient Ck;$k and 6k=Q-Kamekawashink of the transversal filter to be realized is calculated and stored in advance.

The term (xm+i, etc.) is supplied to a transversal filter TF which processes it by a coefficient Ck, and the term (xm-antim) is supplied to a transversal filter TF' which processes it by a coefficient 6k.

TF and TF' respectively generate modulo p-operated terms Zm and Zm expressed by the following equations. Zm=★sa. (Xm
-n+22(q-1)-total m-n)(bn+22(q・
1)-jin)Zm:★Tobi. (Xm-n+22(q-・)
- total m-n) (bn122(q.1)-jn) The sample components ym and addition of the waveformed desired signal are obtained by modulo p addition and modulo p subtraction of the terms Zm and Zm.

The transversal fill shown in FIG. 2 can be implemented in various configurations.

The transversal filter shown in FIG. 3 will be explained.

The outputs of ADI and AD2 consist of N word locations, each with N
shift o registers SR3 and SR4 with taps
The signals from each of the above taps are fed to a corresponding one of the modulo p multipliers M, to M, and the second input of these modulo p multipliers is SR.
For SR4 it receives one of the coefficients 6k and for SR4 it receives one of the coefficients 6k. zm and? The outputs from each multiplier are summed to obtain m. Component ym is obtained by adding Zm and Zm modulo p in AD3 and shifting each bit of the result by 2q-1 bit positions in SR', and component m is obtained by subtracting Zm and Zm modulo p in AD4. obtained by. Although transversal filters can also take the form of a built-in function operator, please be aware of the fact that each term to be processed has been represented in Fermat's number system to proceed with the calculation. have to pay.

A modification of the primitive line transformation, that is, the Fermat transformation, which is also related to the Mersenne transformation, is used in this case.

The Fermat transform converts a series of numbers {xn} of length p into X. :《
2kuq+u)・1×20hi》(7) n=0 m1
It can be converted into the term sequence {Xk} defined by .

However, the value in double parentheses is the value obtained for modulo p=22q11. ) The theory of absorption can also be applied to this transformation. In other words, if {Xk} and {Bk} are obtained by converting {xn} and {bn}, then the product analogy of a corresponding pair of converted terms of the converted terms obtained by converting the terms x n and bn singly Transformation term sequence {Yk} consisting of Yk=《Xk・Bk》
The inverse transformation term sequence {yn} is y. =《2 Sanko mo-ゞ＜m・0
＞-b》.

However, the term between <> is the term obtained by the modulus o2q+1-1. Therefore, the two sequences {xn} and {b
The Fermat transform can be advantageously used to reduce the required computational power when determining the convolution function value.

However, in this case, the function D in particular is a complex sequence {
xn 10 i father} and {bn+i6n} can be processed. If {×k} and {father k} and {Bk} and {effect k} are Fermat transform sequences of the sequence {xn} and {table n} and {6n} and {bn}, then two complex number sequences The Fermat transformation sequence of {《xk ten meals k》} and {
It is expressed as 《Bk》iB》》. Considering the above-mentioned transformation attributes, the Fermat-transformed signal of the filtered (corrected) signal is expressed as follows: Yk+Pk=《
It is expressed as k 〆k〆k]・[Bk 〆k]》.

From this formula, Yk:XkBk-XkBk Yk: XkBk ten XkBk becomes.

In this), since j is a real number, the following operation (Xk-Pk) (Bk-jBk
) (Xk+Pk)(Bk+jBk), and by simple binary addition of this operation result, Yk and Y
k can be found.

The desired filter configuration based on the above description is shown in FIG.

The terms xm+i and xm-Jxm are individually combined into Fermat transform operators FMTI and FMT2, from which Xk+〆k and xk-j are respectively generated. ×
k1i and xk-j are supplied to multipliers MULTI and MULT2 which receive the Fermat transform values Ck and 6k of the respective wave coefficients of the filters ↑F and TF' to be realized. Each convolution calculation value from these multipliers is supplied to the corresponding inverse Fermat transform calculation units IFTI and IFT2, and Zm and Zm are generated from these calculation units.
Zm and Zm are supplied to adder AD3 and subtractor AD4 and shift register SR'. Afterwards, each filtered sample ym and Cm becomes SR' and A, respectively.
It is obtained from the output of D4. Filter processing requires non-periodic convolution calculation processing, but if Mersenne transformation, Fermat transformation, or Primitive Wolf transformation is used, this can be achieved by circular convolution calculation processing.

Techniques have been developed to solve this problem, which are summarized below. A data sequence to be subjected to wave processing is divided into blocks of finite length, and each block is appended with the required number of terms equal to zero. Under the selected transformation, perform a shield rotation>conclusion operation for each of the groups thus formed. The terms from two successive shield convolution operations are added to produce the desired non-periodic convolution terms. The transversal filter used in the circuit of FIG. 4 is shown in FIG. 4A.

This is shown in the diagram. Furthermore, a circuit placed between A and B (or between C and D) in FIG. 4 is shown in FIG. 4A. Switch S is used to alternately supply data blocks to supply scales 1 and 2. The required number of zeros is added to each block before it is sent to a computing unit FMT' or FMT'' which performs the operation of the desired transformation (eg Fermat transformation).
The outputs from Mr and FMT'' are provided to the corresponding multipliers
each output term in the bill calculator is stored in memory M old M
It is multiplied by Ck (or Ck) supplied from. Sequential outputs from these multipliers are added term by term in an adder +, and the output from the adder is supplied to an arithmetic unit IFT that performs inverse transformation. As mentioned above, multiplying a word by j means that in Fermat's number system, each bit of the word is multiplied by 2.
This is equivalent to shifting by (q-1) bit positions.

Therefore, any jX term is somewhat longer than X. Since the advantage of a processor using a conversion process is practically limited by the length of the word to be converted, the converters FMTI and FM
These transducers are preferably placed so that T2 processes {xm} and {2m} directly. FIG. 5 shows a configuration in which filter processing is performed under variable filter coefficients. Input signal sequence {xn}
and {table n} and filter coefficient sequence {bn} and {6n
} are the formal conversion calculators FMT1, FMT2, F, respectively.
It is supplied to MT'1 and FMr2. FMT2 and FM
The output of T'2 is the shift register SR or SRO.
is multiplied by j using . These results are based on FMTI and FM
It is subtracted from these outputs while being added to the outputs of T'1. Multipliers MULTI and MULT2 are respectively ADI
and the terms from AD'1 are multiplied by the terms from AD2 and A02.

After that, the output of MULTI and MULT2 becomes AD'3
is added, A〇4 is subtracted, A〇3 and AD'
From 4, the terms kBk-xkK and XkBk+XkBk are generated, respectively, and these terms are converted to 1 and IFT by the inverse Fermat transform operator IF which generates the outputs ym and Cm, respectively.
'2. The above precautions regarding circular and non-interval incorporation operations are equally applicable to the filter shown in FIG. Among the various components of the filter illustrated in FIGS. 4 and 5, except for the fermat transform calculator and the inverse fermat calculator, the remaining components are all of the same type.

However, since the primitive root transformation can be changed to the Fermat transformation, it is possible to use a primitive root transformation operator. This primitive root conversion arithmetic unit is generated by successively accumulating multiple terms of each term an of the term sequence {an}, and generates a primitive root transformation term sequence by successively accumulating these multiple terms. In addition to this, the Fermat transform is very similar to the Mersenne transform and is therefore
Compute Vol.C121, No.12
, Dhi cem r l972, pp 1269-127
3) “Discrete Convolution”
m via Mersenne Tramforms
The devices shown in Figures 1 and 2 of the paper published under the title ``1.

The processor of FIG. 5 using variable coefficients may implement an equalizer particularly used in the transmission field.

[Brief explanation of drawings]

FIG. 1 is a diagram showing a complex signal filter according to the prior art, FIGS. 2 and 3 are diagrams showing a complex signal filter according to the present invention, and FIGS. 4, 4A, and 5 are diagrams showing a complex signal filter according to the present invention. It is a figure showing the filter used. ADI and AD3... Adder, AD2 and AD
4... ．． ．． Subtractor, TF and TF'...Transversal filter, SR and SR...Shift
register. FIG. 5FIG. 2 FIG.5 FIG. 4 FIG. 4A

Claims (1)

[Claims] 1 A digital filter of the type that receives real and imaginary component samples of a complex signal to be filtered and separately generates real and imaginary components of the complex signal to be filtered, Delay processing of the sample so that the sample of the imaginary component of the signal is multiplied by j (where J is the imaginary unit √(-1) and is expressed by the square of a certain real number to the power of 2 in the Fermat number system) a first means for adding the real component samples of the complex signal to be filtered and the imaginary component samples multiplied by j; and a second means for adding the real component samples of the complex signal to be filtered. third means for subtracting said j times multiplied imaginary component sample; fourth means for individually applying the signals supplied by said second and third means to transversal filter means; fifth means for adding together the signals from the second and third means that have passed through the universal filter means;
sixth means for subtracting the signals from said second and third means through a filter means; and delaying said result so as to multiply the result of the addition performed by said fifth means by a factor of j. and seventh means for performing processing.